The use of random samples to approximate properties of geometric configurations has been an influential idea for both combinatorial and algorithmic purposes. This chapter considers two related notions—ǫ-approximations and ǫ-nets—that capture the most important quantitative properties that one would expect from a random sample with respect to an underlying geometric configuration. An example pro...

We give a $(1+\epsilon)$-approximate distance oracle with $O(1)$ query time for an undirected planar graph $G$ with $n$ vertices and non-negative edge lengths. For $\epsilon>0$ and any two vertices $u$ and $v$ in $G$, our oracle gives a distance $\tilde{d}(u,v)$ with stretch $(1+\epsilon)$ in $O(1)$ time. The oracle has size $O(n\log n ((\log n)/\epsilon+f(\epsilon)))$ and pre-processing time $...

We developed a method to estimate genotype-specific average relative mortality risk, R, from genotype distributions in cross-sectional studies of people belonging to different age-groups, and applied the method to new data from a study of apolipoprotein E genotypes (apoE) in 177 Danish centenarians and data from a study of 40-year-old Danish men. Twenty-one percent of the centenarians were epsi...

Genotoxic activities of a series of commercially purchased 1,N6-ethenoadenosine (epsilon-Ado) and epsilon-deoxyadenosine (epsilon-dAdo) derivatives were assessed using the sister chromatid exchange (SCE) assay in murine spleen lymphocytes in vitro. Of the epsilon-Ado adducts evaluated for SCE induction epsilon-ATP and epsilon-dATP were highly active (5x baseline) SCE inducers over a concentrati...

We review the current status of calculations of the two pion decays of the kaon using the firstprinciples methods of lattice gauge theory and the significant challenges that these calculations pose. While a calculation with controlled errors at even the 10-20% level has not yet been performed, present results suggest that such a calculation of the real and imaginary parts of the ∆I = 3/2 amplit...

vspace{0.2cm}In this paper, we design a data structure for the following problem. Let $pi$ be an $x$-monotone trajectory with $n$ vertices in the plane and $epsilon >0$. We show how to preprocess $pi$ and $epsilon$ into a data structure such that for any horizontal query segment $Q$ in the plane, one can quickly determine the minimal continuous fraction of $pi$ whose Fr{'e}chet and Hausdo...

The use of random samples to approximate properties of geometric configurations has been an influential idea for both combinatorial and algorithmic purposes. This chapter considers two related notions— -approximations and -nets—that capture the most important quantitative properties that one would expect from a random sample with respect to an underlying geometric configuration. An example prob...

A population of cells that express mast cell markers, including the membrane protein p161, but that lack expression of the high affinity IgE receptor, Fc epsilon RI, can be routinely grown from bone marrow. Ionomycin, but not IgE immune complexes, causes these cells to release serotonin and to express IL-3 and IL-13 mRNA, consistent with their being FC epsilon RI-deficient mast cells. These p16...

We present extensive molecular dynamics simulation results for the structure and the static and dynamical responses of a droplet of 1000 soft spheres carrying extended dipoles and confined to spherical cavities of radii R=2.5, 3, and 4 nm embedded in a dielectric continuum of permittivity epsilon(')>or=1. The polarization of the external medium by the charge distribution inside the cavity is ac...

Protein kinase C (PKC) plays a prominent role in immune signaling, and the paradigms for isoform selective signaling are beginning to be elucidated. Real-time microscopy was combined with molecular and biochemical approaches to demonstrate a role for PKC- epsilon in Fc gamma receptor (Fc gammaR)-dependent phagocytosis. RAW 264.7 macrophages were transfected with GFP-conjugated PKC isoforms, and...